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Machine-Level Programming IV: Structured Data

Machine-Level Programming IV: Structured Data. Topics Arrays Structs Unions. Basic Data Types. Integral Stored & operated on in general registers Signed vs. unsigned depends on instructions used Intel GAS Bytes C byte b 1 [ unsigned ] char word w 2 [ unsigned ] short

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Machine-Level Programming IV: Structured Data

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  1. Machine-Level Programming IV:Structured Data • Topics • Arrays • Structs • Unions

  2. Basic Data Types • Integral • Stored & operated on in general registers • Signed vs. unsigned depends on instructions used Intel GAS Bytes C byte b 1 [unsigned] char word w 2 [unsigned] short double word l 4 [unsigned] int • Floating Point • Stored & operated on in floating point registers Intel GAS Bytes C Single s 4 float Double l 8 double Extended t 10/12 long double

  3. char string[12]; x x + 12 int val[5]; double a[4]; x x + 4 x + 8 x + 12 x + 16 x + 20 x x + 8 x + 16 x + 24 x + 32 x x + 4 x + 8 Array Allocation • Basic Principle TA[L]; • Array of data type T and length L • Contiguously allocated region of L * sizeof(T) bytes char *p[3];

  4. int val[5]; 1 5 2 1 3 x x + 4 x + 8 x + 12 x + 16 x + 20 Array Access • Basic Principle TA[L]; • Array of data type T and length L • Identifier A can be used as a pointer to array element 0 • Reference Type Value val[4] int 3 val int * x val+1int * x + 4 &val[2]int * x + 8 val[5]int ?? *(val+1)int 5 val + iint * x + 4 i

  5. zip_dig cmu; zip_dig ucb; zip_dig mit; 0 1 9 4 5 2 1 7 2 2 3 1 9 0 3 36 16 56 40 60 20 24 64 44 28 68 48 32 52 72 76 36 56 Array Example typedef int zip_dig[5]; zip_dig cmu = { 1, 5, 2, 1, 3 }; zip_dig mit = { 0, 2, 1, 3, 9 }; zip_dig ucb = { 9, 4, 7, 2, 0 }; • Notes • Declaration “zip_dig cmu” equivalent to “int cmu[5]” • Example arrays were allocated in successive 20 byte blocks • Not guaranteed to happen in general

  6. Array Accessing Example • Computation • Register %edx contains starting address of array • Register %eax contains array index • Desired digit at 4*%eax + %edx • Use memory reference (%edx,%eax,4) • Memory Reference Code int get_digit (zip_dig z, int dig) { return z[dig]; } # %edx = z # %eax = dig movl (%edx,%eax,4),%eax # z[dig]

  7. zip_dig cmu; zip_dig mit; zip_dig ucb; 1 0 9 2 5 4 7 1 2 2 1 3 9 0 3 36 16 56 40 20 60 44 24 64 68 48 28 32 72 52 56 36 76 Referencing Examples • Code Does Not Do Any Bounds Checking! • Reference Address Value Guaranteed? mit[3] 36 + 4* 3 = 48 3 mit[5] 36 + 4* 5 = 56 9 mit[-1] 36 + 4*-1 = 32 3 cmu[15] 16 + 4*15 = 76 ?? • Out of range behavior implementation-dependent • No guaranteed relative allocation of different arrays Yes No No No

  8. Array Loop Example int zd2int(zip_dig z) { int i; int zi = 0; for (i = 0; i < 5; i++) { zi = 10 * zi + z[i]; } return zi; } • Original Source • Transformed Version • As generated by GCC • Eliminate loop variable i • Convert array code to pointer code • Express in do-while form • No need to test at entrance int zd2int(zip_dig z) { int zi = 0; int *zend = z + 4; do { zi = 10 * zi + *z; z++; } while(z <= zend); return zi; }

  9. Array Loop Implementation int zd2int(zip_dig z) { int zi = 0; int *zend = z + 4; do { zi = 10 * zi + *z; z++; } while(z <= zend); return zi; } int zd2int(zip_dig z) { int zi = 0; int *zend = z + 4; do { zi = 10 * zi + *z; z++; } while(z <= zend); return zi; } int zd2int(zip_dig z) { int zi = 0; int *zend = z + 4; do { zi = 10 * zi + *z; z++; } while(z <= zend); return zi; } int zd2int(zip_dig z) { int zi = 0; int *zend = z + 4; do { zi = 10 * zi + *z; z++; } while(z <= zend); return zi; } int zd2int(zip_dig z) { int zi = 0; int *zend = z + 4; do { zi = 10 * zi + *z; z++; } while(z <= zend); return zi; } • Registers %ecx z %eax zi %ebx zend • Computations • 10*zi + *z implemented as *z + 2*(zi+4*zi) • z++ increments by 4 # %ecx = z xorl %eax,%eax # zi = 0 leal 16(%ecx),%ebx # zend = z+4 .L59: leal (%eax,%eax,4),%edx # 5*zi movl (%ecx),%eax # *z addl $4,%ecx # z++ leal (%eax,%edx,2),%eax # zi = *z + 2*(5*zi) cmpl %ebx,%ecx # z : zend jle .L59 # if <= goto loop # %ecx = z xorl %eax,%eax # zi = 0 leal 16(%ecx),%ebx # zend = z+4 .L59: leal (%eax,%eax,4),%edx # 5*zi movl (%ecx),%eax # *z addl $4,%ecx # z++ leal (%eax,%edx,2),%eax # zi = *z + 2*(5*zi) cmpl %ebx,%ecx # z : zend jle .L59 # if <= goto loop # %ecx = z xorl %eax,%eax # zi = 0 leal 16(%ecx),%ebx # zend = z+4 .L59: leal (%eax,%eax,4),%edx # 5*zi movl (%ecx),%eax # *z addl $4,%ecx # z++ leal (%eax,%edx,2),%eax # zi = *z + 2*(5*zi) cmpl %ebx,%ecx # z : zend jle .L59 # if <= goto loop # %ecx = z xorl %eax,%eax # zi = 0 leal 16(%ecx),%ebx # zend = z+4 .L59: leal (%eax,%eax,4),%edx # 5*zi movl (%ecx),%eax # *z addl $4,%ecx # z++ leal (%eax,%edx,2),%eax # zi = *z + 2*(5*zi) cmpl %ebx,%ecx # z : zend jle .L59 # if <= goto loop # %ecx = z xorl %eax,%eax # zi = 0 leal 16(%ecx),%ebx # zend = z+4 .L59: leal (%eax,%eax,4),%edx # 5*zi movl (%ecx),%eax # *z addl $4,%ecx # z++ leal (%eax,%edx,2),%eax # zi = *z + 2*(5*zi) cmpl %ebx,%ecx # z : zend jle .L59 # if <= goto loop

  10. zip_dig pgh[4]; 1 1 1 1 5 5 5 5 2 2 2 2 1 2 0 1 7 1 6 3 76 96 116 136 156 Nested Array Example #define PCOUNT 4 zip_dig pgh[PCOUNT] = {{1, 5, 2, 0, 6}, {1, 5, 2, 1, 3 }, {1, 5, 2, 1, 7 }, {1, 5, 2, 2, 1 }}; • Declaration “zip_dig pgh[4]” equivalent to “int pgh[4][5]” • Variable pgh denotes array of 4 elements • Allocated contiguously • Each element is an array of 5 int’s • Allocated contiguously • “Row-Major” ordering of all elements guaranteed

  11. A[0][0] • • • A[0][C-1] • • • • • • •  •  • • • • • • • A [0] [0] • • • A [R-1] [0] A [1] [0] A [0] [C-1] A [1] [C-1] A [R-1] [C-1] A[R-1][0] • • • A[R-1][C-1] Nested Array Allocation • Declaration TA[R][C]; • Array of data type T • R rows, C columns • Type T element requires K bytes • Array Size • R * C * K bytes • Arrangement • Row-Major Ordering int A[R][C]; 4*R*C Bytes

  12. A[0] A[i] A[R-1] • • • A [i] [0] • • • A [R-1] [0] A [0] [0] • • • A [0] [C-1] A [i] [C-1] A [R-1] [C-1] Nested Array Row Access • Row Vectors • A[i] is array of C elements • Each element of type T • Starting address A + i * C * K int A[R][C]; •  •  • •  •  • A A+i*C*4 A+(R-1)*C*4

  13. Nested Array Row Access Code int *get_pgh_zip(int index) { return pgh[index]; } • Row Vector • pgh[index] is array of 5 int’s • Starting address pgh+20*index • Code • Computes and returns address • Compute as pgh + 4*(index+4*index) # %eax = index leal (%eax,%eax,4),%eax # 5 * index leal pgh(,%eax,4),%eax # pgh + (20 * index)

  14. A[0] A[R-1] • • • • • • A [R-1] [0] A [0] [0] A [R-1] [C-1] A [0] [C-1] Nested Array Element Access • Array Elements • A[i][j] is element of type T • Address A + (i * C + j) * K A [i] [j] int A[R][C]; A[i] •  •  • • • • • • • A [i] [j] •  •  • A A+i*C*4 A+(R-1)*C*4 A+(i*C+j)*4

  15. Nested Array Element Access Code • Array Elements • pgh[index][dig] is int • Address: pgh + 20*index + 4*dig • Code • Computes address pgh + 4*dig + 4*(index+4*index) • movl performs memory reference int get_pgh_digit (int index, int dig) { return pgh[index][dig]; } # %ecx = dig # %eax = index leal 0(,%ecx,4),%edx # 4*dig leal (%eax,%eax,4),%eax # 5*index movl pgh(%edx,%eax,4),%eax # *(pgh + 4*dig + 20*index)

  16. 9 1 0 4 2 5 7 1 2 1 2 3 3 9 0 cmu 36 56 16 60 40 20 44 64 24 68 48 28 32 72 52 36 56 76 univ 160 36 mit 164 16 ucb 168 56 Multi-Level Array Example • Variable univ denotes array of 3 elements • Each element is a pointer • 4 bytes • Each pointer points to array of int’s zip_dig cmu = { 1, 5, 2, 1, 3 }; zip_dig mit = { 0, 2, 1, 3, 9 }; zip_dig ucb = { 9, 4, 7, 2, 0 }; #define UCOUNT 3 int *univ[UCOUNT] = {mit, cmu, ucb};

  17. Element Access in Multi-Level Array int get_univ_digit (int index, int dig) { return univ[index][dig]; } • Computation • Element access Mem[Mem[univ+4*index]+4*dig] • Must do two memory reads • First get pointer to row array • Then access element within array # %ecx = index # %eax = dig leal 0(,%ecx,4),%edx # 4*index movl univ(%edx),%edx # Mem[univ+4*index] movl (%edx,%eax,4),%eax # Mem[...+4*dig]

  18. Similar C references Nested Array Element at Mem[pgh+20*index+4*dig] Different address computation Multi-Level Array Element at Mem[Mem[univ+4*index]+4*dig] Array Element Accesses int get_pgh_digit (int index, int dig) { return pgh[index][dig]; } int get_univ_digit (int index, int dig) { return univ[index][dig]; }

  19. (*,k) (i,*) Row-wise A B Column-wise Using Nested Arrays #define N 16 typedef int fix_matrix[N][N]; • Strengths • C compiler handles doubly subscripted arrays • Generates very efficient code • Avoids multiply in index computation • Limitation • Only works if have fixed array size /* Compute element i,k of fixed matrix product */ int fix_prod_ele (fix_matrix a, fix_matrix b, int i, int k) { int j; int result = 0; for (j = 0; j < N; j++) result += a[i][j]*b[j][k]; return result; }

  20. Dynamic Nested Arrays int * new_var_matrix(int n) { return (int *) calloc(sizeof(int), n*n); } • Strength • Can create matrix of arbitrary size • Programming • Must do index computation explicitly • Performance • Accessing single element costly • Must do multiplication int var_ele (int *a, int i, int j, int n) { return a[i*n+j]; } movl 12(%ebp),%eax # i movl 8(%ebp),%edx # a imull 20(%ebp),%eax # n*i addl 16(%ebp),%eax # n*i+j movl (%edx,%eax,4),%eax # Mem[a+4*(i*n+j)]

  21. (*,k) (i,*) Row-wise A B Column-wise Dynamic Array Multiplication /* Compute element i,k of variable matrix product */ int var_prod_ele (int *a, int *b, int i, int k, int n) { int j; int result = 0; for (j = 0; j < n; j++) result += a[i*n+j] * b[j*n+k]; return result; } • Without Optimizations • Multiplies • 2 for subscripts • 1 for data • Adds • 4 for array indexing • 1 for loop index • 1 for data

  22. Optimizing Dynamic Array Mult. { int j; int result = 0; for (j = 0; j < n; j++) result += a[i*n+j] * b[j*n+k]; return result; } • Optimizations • Performed when set optimization level to -O2 • Code Motion • Expression i*n can be computed outside loop • Strength Reduction • Incrementing j has effect of incrementing j*n+k by n • Performance • Compiler can optimize regular access patterns { int j; int result = 0; int iTn = i*n; int jTnPk = k; for (j = 0; j < n; j++) { result += a[iTn+j] * b[jTnPk]; jTnPk += n; } return result; }

  23. i a p 20 0 4 16 Structures • Concept • Contiguously-allocated region of memory • Refer to members within structure by names • Members may be of different types • Accessing Structure Member struct rec { int i; int a[3]; int *p; }; Memory Layout Assembly void set_i(struct rec *r, int val) { r->i = val; } # %eax = val # %edx = r movl %eax,(%edx) # Mem[r] = val

  24. Generating Pointer to Struct. Member r struct rec { int i; int a[3]; int *p; }; • Generating Pointer to Array Element • Offset of each structure member determined at compile time i a p 0 4 16 r + 4 + 4*idx int * find_a (struct rec *r, int idx) { return &r->a[idx]; } # %ecx = idx # %edx = r leal 0(,%ecx,4),%eax # 4*idx leal 4(%eax,%edx),%eax # r+4*idx+4

  25. Element i i i a a p 0 0 4 4 16 16 Structure Referencing (Cont.) • C Code struct rec { int i; int a[3]; int *p; }; void set_p(struct rec *r) { r->p = &r->a[r->i]; } # %edx = r movl (%edx),%ecx # r->i leal 0(,%ecx,4),%eax # 4*(r->i) leal 4(%edx,%eax),%eax # r+4+4*(r->i) movl %eax,16(%edx) # Update r->p

  26. Alignment • Aligned Data • Primitive data type requires K bytes • Address must be multiple of K • Required on some machines; advised on IA32 • treated differently by Linux and Windows! • Motivation for Aligning Data • Memory accessed by (aligned) double or quad-words • Inefficient to load or store datum that spans quad word boundaries • Virtual memory very tricky when datum spans 2 pages • Compiler • Inserts gaps in structure to ensure correct alignment of fields

  27. Specific Cases of Alignment • Size of Primitive Data Type: • 1 byte (e.g., char) • no restrictions on address • 2 bytes (e.g., short) • lowest 1 bit of address must be 02 • 4 bytes (e.g., int, float, char *, etc.) • lowest 2 bits of address must be 002 • 8 bytes (e.g., double) • Windows (and most other OS’s & instruction sets): • lowest 3 bits of address must be 0002 • Linux: • lowest 2 bits of address must be 002 • i.e., treated the same as a 4-byte primitive data type • 12 bytes (long double) • Linux: • lowest 2 bits of address must be 002 • i.e., treated the same as a 4-byte primitive data type

  28. Satisfying Alignment with Structures • Offsets Within Structure • Must satisfy element’s alignment requirement • Overall Structure Placement • Each structure has alignment requirement K • Largest alignment of any element • Initial address & structure length must be multiples of K • Example (under Windows): • K = 8, due to double element struct S1 { char c; int i[2]; double v; } *p; c i[0] i[1] v p+0 p+4 p+8 p+16 p+24 Multiple of 4 Multiple of 8 Multiple of 8 Multiple of 8

  29. c i[0] i[1] v p+0 p+4 p+8 p+16 p+24 Multiple of 4 Multiple of 8 Multiple of 8 Multiple of 8 c i[0] i[1] v p+0 p+4 p+8 p+12 p+20 Multiple of 4 Multiple of 4 Multiple of 4 Multiple of 4 Linux vs. Windows struct S1 { char c; int i[2]; double v; } *p; • Windows (including Cygwin): • K = 8, due to double element • Linux: • K = 4; double treated like a 4-byte data type

  30. x i[0] i[1] c p+0 p+8 p+12 p+16 Windows: p+24 Linux: p+20 x[0] x[1] i[0] i[1] c p+0 p+4 p+8 p+12 p+16 p+20 Overall Alignment Requirement struct S2 { double x; int i[2]; char c; } *p; p must be multiple of: 8 for Windows 4 for Linux struct S3 { float x[2]; int i[2]; char c; } *p; p must be multiple of 4 (in either OS)

  31. c1 v c2 i p+0 p+8 p+16 p+20 p+24 v c1 c2 i p+0 p+8 p+12 p+16 Ordering Elements Within Structure struct S4 { char c1; double v; char c2; int i; } *p; 10 bytes wasted space in Windows struct S5 { double v; char c1; char c2; int i; } *p; 2 bytes wasted space

  32. a[1].i a[1].v a[1].j • • • a[0] a[1] a[2] a+0 a+12 a+24 a+36 Arrays of Structures • Principle • Allocated by repeating allocation for array type • In general, may nest arrays & structures to arbitrary depth struct S6 { short i; float v; short j; } a[10]; a+12 a+16 a+20 a+24

  33. a[i].i a[i].v a[i].j a[0] • • • a[i] • • • a+12i a+0 Accessing Element within Array • Compute offset to start of structure • Compute 12*i as 4*(i+2i) • Access element according to its offset within structure • Offset by 8 • Assembler gives displacement as a + 8 • Linker must set actual value struct S6 { short i; float v; short j; } a[10]; short get_j(int idx) { return a[idx].j; } # %eax = idx leal (%eax,%eax,2),%eax # 3*idx movswl a+8(,%eax,4),%eax a+12i a+12i+8

  34. a[0] • • • a[i] • • • a+12i a+0 a[1].i a[1].v a[1].j a+12i a+12i+4 Satisfying Alignment within Structure • Achieving Alignment • Starting address of structure array must be multiple of worst-case alignment for any element • a must be multiple of 4 • Offset of element within structure must be multiple of element’s alignment requirement • v’s offset of 4 is a multiple of 4 • Overall size of structure must be multiple of worst-case alignment for any element • Structure padded with unused space to be 12 bytes struct S6 { short i; float v; short j; } a[10]; Multiple of 4 Multiple of 4

  35. c i[0] i[1] c i[0] i[1] v v up+0 up+4 up+8 sp+0 sp+4 sp+8 sp+16 sp+24 Union Allocation • Principles • Overlay union elements • Allocate according to largest element • Can only use one field at a time union U1 { char c; int i[2]; double v; } *up; struct S1 { char c; int i[2]; double v; } *sp; (Windows alignment)

  36. Using Union to Access Bit Patterns typedef union { float f; unsigned u; } bit_float_t; float bit2float(unsigned u) { bit_float_t arg; arg.u = u; return arg.f; } • Get direct access to bit representation of float • bit2float generates float with given bit pattern • NOT the same as (float) u • float2bit generates bit pattern from float • NOT the same as (unsigned) f u f unsigned float2bit(float f) { bit_float_t arg; arg.f = f; return arg.u; } 0 4

  37. Byte Ordering Revisited • Idea • Short/long/quad words stored in memory as 2/4/8 consecutive bytes • Which is most (least) significant? • Can cause problems when exchanging binary data between machines • Big Endian • Most significant byte has lowest address • PowerPC, Sparc • Little Endian • Least significant byte has lowest address • Intel x86, Alpha

  38. Byte Ordering Example union { unsigned char c[8]; unsigned short s[4]; unsigned int i[2]; unsigned long l[1]; } dw; c[0] c[1] c[2] c[3] c[4] c[5] c[6] c[7] s[0] s[1] s[2] s[3] i[0] i[1] l[0]

  39. Byte Ordering Example (Cont). int j; for (j = 0; j < 8; j++) dw.c[j] = 0xf0 + j; printf("Characters 0-7 == [0x%x,0x%x,0x%x,0x%x,0x%x,0x%x,0x%x,0x%x]\n", dw.c[0], dw.c[1], dw.c[2], dw.c[3], dw.c[4], dw.c[5], dw.c[6], dw.c[7]); printf("Shorts 0-3 == [0x%x,0x%x,0x%x,0x%x]\n", dw.s[0], dw.s[1], dw.s[2], dw.s[3]); printf("Ints 0-1 == [0x%x,0x%x]\n", dw.i[0], dw.i[1]); printf("Long 0 == [0x%lx]\n", dw.l[0]);

  40. f0 f1 f2 f3 f4 f5 f6 f7 c[0] c[1] c[2] c[3] c[4] c[5] c[6] c[7] LSB MSB LSB MSB LSB MSB LSB MSB s[0] s[1] s[2] s[3] LSB MSB LSB MSB i[0] i[1] LSB MSB l[0] Print Byte Ordering on x86 Little Endian Output on Pentium: Characters 0-7 == [0xf0,0xf1,0xf2,0xf3,0xf4,0xf5,0xf6,0xf7] Shorts 0-3 == [0xf1f0,0xf3f2,0xf5f4,0xf7f6] Ints 0-1 == [0xf3f2f1f0,0xf7f6f5f4] Long 0 == [f3f2f1f0]

  41. f0 f1 f2 f3 f4 f5 f6 f7 c[0] c[1] c[2] c[3] c[4] c[5] c[6] c[7] MSB LSB MSB LSB MSB LSB MSB LSB s[0] s[1] s[2] s[3] MSB LSB MSB LSB i[0] i[1] MSB LSB l[0] Print Byte Ordering on Sun Big Endian Output on Sun: Characters 0-7 == [0xf0,0xf1,0xf2,0xf3,0xf4,0xf5,0xf6,0xf7] Shorts 0-3 == [0xf0f1,0xf2f3,0xf4f5,0xf6f7] Ints 0-1 == [0xf0f1f2f3,0xf4f5f6f7] Long 0 == [0xf0f1f2f3]

  42. f0 f1 f2 f3 f4 f5 f6 f7 c[0] c[1] c[2] c[3] c[4] c[5] c[6] c[7] LSB MSB LSB MSB LSB MSB LSB MSB s[0] s[1] s[2] s[3] LSB MSB LSB MSB i[0] i[1] LSB MSB l[0] Print Byte Ordering on Alpha Little Endian Output on Alpha: Characters 0-7 == [0xf0,0xf1,0xf2,0xf3,0xf4,0xf5,0xf6,0xf7] Shorts 0-3 == [0xf1f0,0xf3f2,0xf5f4,0xf7f6] Ints 0-1 == [0xf3f2f1f0,0xf7f6f5f4] Long 0 == [0xf7f6f5f4f3f2f1f0]

  43. Summary • Arrays in C • Contiguous allocation of memory • Pointer to first element • No bounds checking • Compiler Optimizations • Compiler often turns array code into pointer code (zd2int) • Uses addressing modes to scale array indices • Lots of tricks to improve array indexing in loops • Structures • Allocate bytes in order declared • Pad in middle and at end to satisfy alignment • Unions • Overlay declarations • Way to circumvent type system

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